Problem: A local gift shop sold bags of candy and cookies for Halloween. Bags of candy cost $$6.00$, and bags of cookies cost $$2.50$, and sales equaled $$38.00$ in total. There were $5$ more bags of cookies than candy sold. Find the number of bags of candy and cookies sold by the gift shop.
Explanation: Let $x$ equal the number of bags of candy and $y$ equal the number of bags of cookies. The system of equations is then: ${6x+2.5y = 38}$ ${y = x+5}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${x+5}$ for $y$ in the first equation. ${6x + 2.5}{(x+5)}{= 38}$ Simplify and solve for $x$ $ 6x+2.5x + 12.5 = 38 $ $ 8.5x+12.5 = 38 $ $ 8.5x = 25.5 $ $ x = \dfrac{25.5}{8.5} $ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $ {y = x+5}$ to find $y$ ${y = }{(3)}{ + 5}$ ${y = 8}$ You can also plug ${x = 3}$ into $ {6x+2.5y = 38}$ and get the same answer for $y$ ${6}{(3)}{ + 2.5y = 38}$ ${y = 8}$ $3$ bags of candy and $8$ bags of cookies were sold.